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Alexander Polynomials of Knots Which Are Transformed into the Trefoil Knot by a Single Crossing Change

Nakanishi, Yasutaka

  • Received : 2009.08.18
  • Accepted : 2012.05.25
  • Published : 2012.06.23

Abstract

By the works of Kondo and Sakai, it is known that Alexander polynomials of knots which are transformed into the trivial knot by a single crossing change are characterized. In this note, we will characterize Alexander polynomials of knots which are transformed into the trefoil knot (and into the figure-eight knot) by a single crossing change.

Keywords

Alexander polynomials;Crossing change;Trefoil knot;Figure-eight knot

References

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Cited by

  1. Differences of Alexander polynomials for knots caused by a single crossing change, II vol.26, pp.14, 2017, https://doi.org/10.1142/S0218216517500973
  2. Knot adjacency from a surgical view of Alexander invariants vol.26, pp.14, 2017, https://doi.org/10.1142/S0218216517500985